Insight into Construction of Tikhonov-Type Regularization for Atmospheric Retrievals

Abstract

In atmospheric science we are confronted with inverse problems arising in applications associated with retrievals of geophysical parameters. A nonlinear mapping from geophysical quantities (e.g., atmospheric properties) to spectral measurements can be represented by a forward model. An inversion often suffers from the lack of stability and its stabilization introduced by proper approaches, however, can be treated with sufficient generality. In principle, regularization can enforce uniqueness of the solution when additional information is incorporated into the inversion process. In this paper, we analyze different forms of the regularization matrix L in the framework of Tikhonov regularization: the identity matrix L0, discrete approximations of the first and second order derivative operators L1 and L2, respectively, and the Cholesky factor of the a priori profile covariance matrix LC. Each form of L has its intrinsic pro/cons and thus may lead to different performance of inverse algorithms. An extensive comparison of different matrices is conducted with two applications using synthetic data from airborne and satellite sensors: retrieving atmospheric temperature profiles from microwave spectral measurements, and deriving aerosol properties from near infrared spectral measurements. The regularized solution obtained with L0 possesses a reasonable magnitude, but its smoothness is not always assured. The retrieval using L1 and L2 produces a solution in favor of the smoothness, and the impact of the a priori knowledge is less critical on the retrieval using L1. The retrieval performance of LC is affected by the accuracy of the a priori knowledge.

China's First Infrared Occultation Spectrometer (GaoFen-5/AIUS) Monitoring Atmosphere Above Antarctic: Evaluation of Methane Profiles

“…When γ → 0, Equations ( 8)-( 9) are similar. For more details on the retrieval procedure, please refer to [16], [29]- [33].…”

Optimization of Aerosol Model Selection for TROPOMI/S5P

“…To speed up the computation in the oxygen absorption band from sensors (e.g., TROPOMI) with very high spectral resolution, we have implemented acceleration techniques like the telescoping technique [27,28], the false discrete ordinate approach, the correlated k-distribution method [29], and the principal components analysis [30,31]. The inversion is performed by the means of Tikhonov regularization with optimal strategies for constructing the regularization parameter and matrix [32,33]. For further details about the retrieval algorithm and its forward model, we refer to the works in [34][35][36].…”

A Proof-of-Concept Algorithm for the Retrieval of Total Column Amount of Trace Gases in a Multi-Dimensional Atmosphere

“…where F : R n → R m is the forward model, x ∈ R n the state vector, and y δ ∈ R m the noisy data vector. In DRMI and DRME, the state vectors are Because the nonlinear Equation ( 19) is usually ill-posed, a regularization method, as, for example, the iteratively regularized Gauss-Newton method, is used to compute a solution with physical meaning [15,20,21]. In this approach, at the iteration step k, we consider a linearization of F(x) around the current iterate x δ k and solve the linearized equation by means of Tikhonov regularization with the penalty term α k ||L(x − x a )|| 2 , where α k is the regularization parameter at the iteration step k, L the regularization matrix, and x a the a priori state vector, the best beforehand estimate of the solution.…”